In Animation Nodes, is it possible to make a node to translate position of the UV's of an instance?
Note: I have replaced the Shader Controller Node (no longer supported) by new Material Attribute Input/Output Nodes, so I have updated this answer.

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Method-1: Offsetting the coordinate in Mapping Node of single texture for different materials:
Here, I have made a simple example to use Material Attribute Input/Output Nodes. These nodes are work similar to Object Attribute Input/Output Nodes,

A simple shader Node-tree:


AN Node-tree for one object:


Now, for multiple objects: I have instanced a cube (with deep copy) and a material then assign them to individual objects by using Object Material Output node in a Loop Node. Then use the same setup of Material Attribute Output Node (mentioned above) to offset coordinates of Mapping Node with Random float node. However, you can use own coordinate list to offset them:


Method-1 Blend File:



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Method-2: Assigning different textures to different materials: In this method, we need a small script which loads a texture from the specified folder then assign to a material. Here is the script:

import bpy

try:
    bpy.data.materials[material.name].node_tree.nodes['Image Texture'].image = bpy.data.images[image]
except:
    filepath = path + image
    newImage = bpy.data.images.load(filepath)
    bpy.data.materials[material.name].node_tree.nodes['Image Texture'].image = newImage 


and in AN, I have used Script Node to use the script,


This script needs three inputs: material, the path to the image folder, and name of the image. Because, we have multiple images, so we going to use Loop Node, here is the setup:


Now, for multiple objects: I have instanced a cube (with deep copy) and a material then assign them to individual objects by using Object Material Output node in a Loop Node. Then use the above setup to assign different textures for different materials,


Method-2 Blend File:



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